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19 de Diciembre, 2014, 6:02

During the next few months the physical interpretation of quantum mechanics was the central theme of all conversations between Bohr and myself. I was then living on the top floor of the Institute, in a cozy little attic flat with slanting walls and windows overlooking the trees at the entrance to Faelled Park. Bohr would often come into my attic late at night, and we constructed all sorts of imaginary experiments to see whether we had really grasped the theory.

In so doing, we discovered that the two of us were trying to resolve the difficulties in rather different ways. Bohr was trying to allow for the simultaneous existence of both particle and wave concepts, holding that, though the two were mutually exclusive, both together were needed for a complete description of atomic processes. I disliked this approach. I wanted to start from the fact that quantum mechanics as we then knew it already imposed a unique physical interpretation of some magnitudes occurring in it-for instance, the time averages of energy, momentum, fluctuations, etc.-so that it looked very much as if we no longer had any freedom with respect to that interpretation. Instead, we would have to try to derive the correct general interpretation by strict logic from the ready-to-hand, more special interpretation.

For that reason I was-certainly quite wrongly-rather unhappy about a brilliant piece of work Max Born had done in Gottingen. In it, he had treated collisions by Schrodinger's method and assumed that the square of the Schrodinger wave function measures, in each point of space and at every instant, the probability of finding an electron in this point at that instant. I fully agreed with Born's thesis as such, but disliked the fact that it looked as if we still had some freedom of interpretation; I was firmly convinced that Born's thesis itself was the necessary consequence of the fixed interpretation of special magnitudes in quantum mechanics. This conviction was strengthened further by two highly informative mathematical studies by Dirac and Jordan.

Generalizations of the Schrodinger wave function and Born"s statistical interpretation of it were incorporated into matrix mechanics and the related q-number theory of Dirac (1925) through what came to be known as transformation theory. Independently of one another, Dirac and Jordan developed this new formalism in late 1926 and published it in early 1927 (Jordan, 1927a,b; Dirac, 1927). 1 In modern notation, which follows Dirac rather than Jordan, the central quantities in transformation theory are complex probability amplitudes <a|b>, which determine the probability of finding the value a for some observable A after finding the value b for some observable B and at the same time govern the transition of a basis of eigenvectors of A to a basis of eigenvectors of B.